Regulation of spike timing in visual cortical circuits

Transcription

1 Regulation of spike timing in visual ortial iruits Paul Tiesinga*, Jean-Mar Fellous and Terrene J. Sejnowski Abstrat A train of ation potentials (a spike train) an arry information in both the average firing rate and the pattern of spikes in the train. But an suh a spike-pattern ode be supported by ortial iruits? Neurons in vitro produe a spike pattern in response to the injetion of a flutuating urrent. However, ortial neurons in vivo are modulated by loal osillatory neuronal ativity and by top-down inputs. In a ortial iruit, preise spike patterns thus reflet the interation between internally generated ativity and sensory information enoded by input spike trains. We review the evidene for preise and reliable spike timing in the ortex and disuss its omputational role. Spike time The time of ourrene of an ation potential, relative to stimulus onset or another event. Spike volleys A set of spikes emitted at approximately the same time (typially with a temporal spread of between 1 and 1 ms) by a pool of neurons. *Physis and Astronomy Department, University of North Carolina at Chapel Hill, North Carolina , USA. Psyhology and Applied Mathematis Departments, University of Arizona at Tuson, Arizona , USA. Computational Neurobiology Laboratory and Howard Hughes Medial Institute at the Salk Institute, La Jolla, California 9237, USA. Division of Biologial Sienes, University of California at San Diego, La Jolla, California, USA. s: tiesinga@physis. un.edu; fellows@ . arizona.edu; terry@salk.edu doi:1.138/nrn2315 Published online 17 January 28 Reliability and preision are two different quantities. When you make an appointment with your friend, she an either keep the appointment or not show up at all. If she does show up, she might or might not be on time. The former unertainty is related to reliability, whereas the latter is related to preision. When the same stimulus waveform is repeatedly injeted at the soma of a neuron in vitro (FIG. 1a), a similar spike train is obtained on eah trial 1,2 (FIG. 1b). When approximately the same number of spikes our on eah trial the neuron is said to be reliable, whereas when the spikes our almost at the same time aross trials it is said to be preise (FIG. 1). For a single neuron, the potential information ontent of preise and reliable spike times is many times larger than that whih is ontained in the firing rate, whih is averaged aross a typial interval of a hundred milliseonds 3 6. The information ontained in spike timing is available immediately, rather than after an averaging period. Furthermore, the timing of patterns of spikes an potentially transmit even more information than the timing of the individual onstituent spikes 3,7. The potential relevane of spike patterns beomes apparent when we onsider neurons at the population level: when a group of similar neurons (a pool ) produes preise and reliable spike trains, the neurons they projet to reeive volleys of synhronous spikes 8,9. This opens up the possibility of ommuniating between different ortial areas through synhronous spike volleys. In ontrast to the in vitro situation desribed above, in the intat ortex most exitatory synapti inputs arrive at the dendrites rather than at the soma (FIG. 1d), and synapti transmission is typially unreliable Furthermore, most of these dendriti inputs are not diretly related to ongoing sensory stimulation; rather, they reflet spatiotemporally strutured internal ativity. Therefore, when the same stimulus is presented repeatedly, the resulting spike trains are usually neither preise nor reliable when they are aligned to the stimulus onset 6. Instead, neural ativity in vivo might be dominated by internally generated omplex reverberations or rhythmi osillations, and preise and reliable spike trains might only emerge after they have been aligned aording to the phase of the osillation (FIG. 1e). Current tehnologies are progressing to the point where it is possible to reord the simultaneous spiking ativity of hundreds of neurons, as well as to manipulate their spike timing 14,15. However, without a theoretial framework for understanding ortial information proessing, suh data might not be easily interpretable. A key to ortial omputations is the integration of feedforward and top-down information, whih ours at the level of the single ortial neuron. In order to fully understand this proess we need to determine the omputational role of preise and reliable spike times. This Review fouses on preisely emitted spike patterns and their theoretial impliations, and aims to set the stage for the large-sale study of ortial information proessing. We review the biophysial mehanisms that are responsible for generating spike patterns and desribe methods for unovering spike patterns in the presene of ortial bakground ativity. Finally, we link the integration of temporally preise synapti inputs in ative dendrites to ommuniation, using spike volleys, within and between ortial areas. nature reviews neurosiene volume 9 february 28 97

2 a b Trials d Injeted urrent Output spike train Feedforward inputs Reurrent inputs e Stimulus Phasealigned Stimulusloked Phaseloked Unreliable Impreise Deteting spike patterns in vitro. A single-neuron spike pattern is a sequene of spike times that either our together in a trial or do not our at all. For example, a neuron an respond to a ertain segment of a stimulus with a pattern omprised of two spikes that are always separated by 18 ms. Analysis of data reorded from a motion-sensitive neuron in the fly brain shows that suh spike pairs provide more than twie the information provided by single spikes 7, suggesting that information is oded in the pattern in addition to in the individual spike times. A first step in evaluating the possible role of spike patterns in ortial slies in vitro is to detet them. For a series of trials, the data an be arranged to form a similarity matrix, and a lustering algorithm an be used to identify spike patterns. Spike patterns have been unovered in experimental data using this proedure 18, whih is illustrated in FIG. 3 for data taken from a model neuron. Output spike train Feedforward information In the ontext of stimulus response iruitry, feedforward information is information that is proessed in a single diretion from sensory input through pereptual analysis to motor output without involving feedbak information flowing bakwards from higher entres to lower entres. Top-down information The flow of information from higher to lower entres, onveying knowledge derived from previous experiene rather than from sensory stimulation. Phase-loked Stimulus-loked Stimulusaligned Figure 1 Stimulus loking in vitro and in vivo. a An in vitro reliability paradigm. A urrent onsisting of many repeats of a short stimulus waveform followed by a period of zero urrent is injeted using an eletrode at the soma. The start of the stimulus is indiated by a red dash. The orresponding output spike train is shown at the bottom. b Trials are aligned with the red dashes (the stimulus waveform is shown at the bottom). When the neuron is stimulus-loked, the spike trains are similar aross trials. When spikes are missing in some trials but not in others, the neuron is onsidered unreliable. When the spike ours but the spike time is variable, the neuron is onsidered impreise (BOX 1). d In vivo, the neuron reeives feedforward inputs and reurrent inputs. When the same stimulus is presented repeatedly (represented by the red dashes), presynapti neurons produe spike trains with repeatable motifs spike patterns that are similar in eah neuron. Aross a population, this input onsists of a sequene of synhronized spike volleys. Reurrent inputs are periodi when the neuron is embedded in an osillatory network. The beginning of eah osillation yle is indiated by the green dashes. Two types of output spike train are shown: a stimulus-loked train and a phaseloked train. e When the neuron is stimulus-loked, preise and reliable spike trains are obtained only when the trials are aligned with stimulus onset. When the neuron is phaseloked, preise and reliable spike trains emerge only when the spike trains are aligned with the start of the osillation yle. What an we learn from spike patterns in vitro? Preision and reliability of in vitro spike trains. When a ortial neuron in a slie preparation is repeatedly injeted with the same urrent waveform it produes preise and reliable spike trains 1. A spike-time histogram generated from the results of multiple trials of either in vitro or model neurons shows transient peaks orresponding to spike alignments, whih are referred to as events (FIG. 2a ). Quantitatively, the reliability of an event is the fration of trials on whih a spike ours at that time 1,16. The response is said to be preise when the standard deviation of the spike times (also referred to as the jitter ) in an event aross trials is small. In priniple preision and reliability are independent quantities, but in pratie they are often related 17. For most experimental data sets it is not straightforward to alulate the preision and reliability beause of bakground noise. There are several different ways to obtain these measurements (BOX 1). Fators affeting reliability and preision. Simple models of an in vitro preparation in whih synapti transmission is bloked and the same somati urrent is injeted repeatedly suggest that impreision is mainly due to variability in the membrane voltage just before the spike, and that this is inversely proportional to the rate of hange of the voltage 19,2. Thus, a preisely timed spike follows a rapidly depolarizing urrent. There are other soures of impreision: the spike threshold an hange with the rate of voltage hange 21 or membrane urrents an be ativated by neuromodulators. As the rate of hange of the membrane voltage generally inreases with the amplitude of the stimulus, the preision should improve as the stimulus amplitude inreases; this has indeed been observed both in vitro 22,23 and in vivo 24,25. In the situation desribed above, trial-to-trial unreliability results from a failure of spiking, whih ours when the membrane voltage does not reah the spike threshold. In this irumstane, the maximum voltage defletion aused by the stimulus is, on average, below the threshold. The probability of spike failure then depends on how far the peak is below the threshold and on how broad the peak is. The following argument shows that spike failure an lead to distint spike patterns. For the model neuron desribed above and in FIG. 3, spikes our at or lose to peaks in the stimulus waveform. When, on a given trial, a peak is missed, the neuron might spike at the next available peak. On a trial in whih the neuron does spike on the first peak, it might not be able to spike on the next peak beause of afterhyperpolarization urrents or other intraellular events. On these two trials the neuron s spikes will orrespond to two distint sequenes of peaks (FIG. 3g). Aross the two trials the neuron will thus produe distint spike patterns 18,26, as observed in vitro 19,23. When there is a prolonged period without spiking on both trials, the voltage trajetories will onverge bak and the same spike pattern will be obtained. Stimulus loking and phase loking. Preision in spike timing depends on a neuron s firing being loked to features of the stimulus, meaning that whenever a feature appears in the stimulus a spike will be produed with a 98 february 28 volume 9

3 a b d Reliability onstant delay 27. For a onstant-urrent pulse, the only feature that a neuron an lok on to is the onset (illustrated for a model neuron in FIG. 4a). For an aperiodi or periodi drive, a spike is more likely to our during Firing rate (Hz) e Sigma (ms) Time segment Figure 2 Calulating the reliability and preision of neural spike trains. a The spike trains shown were obtained from simulations of a model neuron with Hodgkin Huxley-type voltage-gated hannels driven by a flutuating urrent 26. Similar trains ould be obtained experimentally from neurons in vitro. The rastergram shown was onstruted by plotting the spike train for eah trial on a separate row, aligned with stimulus onset. The y ordinate of eah tik is the trial number and the x ordinate is the spike time relative to the stimulus onset. For further analysis the data were divided into segments (shown in different olours). b Twenty trials from part a from the time interval between 1 and 35 ms relative to the stimulus onset, showing that preision and reliability are distint quantities. Event 1 is reliable that is, a spike ours on eah trial but it is not preise (there is a large jitter). Event 2 is preise but not reliable. Event 3 is both preise and reliable. Spike-time histogram, showing how the average firing rate (the number of spikes per seond) aross a series of trials hanges with time. Events (blue stars) are peaks in the histogram and event reliability is the area under the peak. A threshold (the green line) is set, to define the events. When the threshold is set too high, unreliable events (suh as event 2) are missed; when it is set too low, noise spikes ould be interpreted as events. For the purpose of the reliability alulation (desribed in a previous publiation; see REF. 135), eah spike is replaed by a waveform of width sigma. The parameter sigma represents the temporal resolution of the spike times. d Reliability as a funtion of sigma. Eah urve is olour-oded to math the olour of the time segment in the rastergram (a) that was used in the alulation. The jitter (the standard deviation of the spike times in an event) orresponds approximately to the value of sigma for whih the reliability beomes more than.5. The preision is equal to 1 divided by the jitter. e The jitter for eah segment. The third segment (shown in red) never intersets.5 and the jitter is not defined. Jitter (ms) ertain time intervals (those in whih there is a brief depolarization) than during others (those in whih there are brief hyperpolarizations) (FIG. 4b,d). This phenomenon is referred to as stimulus loking (or phase loking when the drive is periodi) 1,2. An in vitro study demonstrated that the strength of stimulus loking ould, in priniple, be inreased in feedforward networks 8. When a pool of similarly responding neurons generates a moderately preise volley as input to the next pool, the volley produed by the latter pool will be more preise. However, this study assumed that synapti transmission from one pool to the next was perfet, and probably overestimated the amount of reliability and preision that would be present in feedforward networks in vivo. Many neurons have a preferred frequeny for stimulus waveforms, whih affets the type of osillation to whih they an phase-lok. For a subthreshold sinusoidal urrent, the amplitude of the voltage defletion will be maximal when the stimulus frequeny mathes the preferred frequeny. This an be demonstrated in vitro by injeting a sinusoidal urrent with a frequeny that hanges slowly aross time. The neuron s membranevoltage osillations will math the instantaneous frequeny of the drive, but the amplitude of the osillations will vary, reahing a maximum when the instantaneous frequeny mathes the preferred frequeny 23,28,29. When the stimulus amplitude is inreased above the spike threshold, the firing rate, reliability and preision will be optimal for stimulus waveforms at the neuron s preferred frequeny. Experiments show that preferred frequenies depend on neuron types 23,3,31. Models predit that the preferred frequeny arises from the dynamis of voltage-gated hannels When a neuron is injeted with a onstant urrent, after a period of adaptation it will produe an approximately periodi spike train. The frequeny of the spike train will be equal to the average firing rate of the neuron (the diret urrent (DC) firing rate), whih depends on the amplitude of the urrent, but this spike train will not be preise aross trials 1 (model results are shown in FIG. 4a). When a small periodi drive is added (FIG. 4b), however, the preision will improve signifiantly when the stimulus frequeny mathes the DC firing rate 19,35,36. This phenomenon ours even when the neuron does not have a subthreshold preferred frequeny. Neuromodulators generally have multiple effets in ortial iruits. For instane, they an hange the DC firing rate of the neuron 37,38 ; this partiular effet an be modelled as an additional depolarizing or hyperpolarizing urrent. Hene, in the model desribed above, neuromodulators an in priniple alter the DC firing rate so that it approximately mathes the osillation frequeny of the network that the neuron is embedded in. This not only improves the preision of the neuron by way of phase loking 32 but also inreases the postsynapti impat of a pool of suh neurons 26. For instane, in a model of odour reognition 39, a group of neurons driven at the same firing rate ahieved spike synhronization by phase loking to a ommon osillation. nature reviews neurosiene volume 9 february 28 99

4 Spike-time histogram A tool for resolving the behaviour of the firing rate as a funtion of time, by averaging aross multiple trials or multiple neurons. Mathematially, it is obtained by ounting the number of spikes in eah time bin and normalizing the ount by the bin width, the number of trials and/or the number of neurons. Event A time-point relative to the stimulus onset during whih a spike is found on a signifiant fration of the trials. What do we know about spike patterns in vivo? Although spike patterns have been found in vitro in response to urrent injetion at the soma, they an only have a role in information proessing if they are also present in vivo. Here we review the evidene for spike patterns in vivo, using the visual system as our fous, and disuss the influene of reeiving temporally oherent synapti inputs due to osillations. Finally, we disuss how the spike timing of a neuron is affeted by dendriti synapti inputs. Evidene for spike-time preision in the visual system. Preise spike firing has been found at almost all levels of the mammalian visual pathway. In an eye-up preparation, retinal ganglion ells produed preise and reliable spike trains in response to a temporally flutuating visual stimulus 24,25,4 42. Preision inreased as stimulus ontrast inreased, beause of an enlargement in the somati amplitude of the inputs. Neurons in the lateral geniulate nuleus, whih are driven by retinal ganglion ells, have been shown to respond preisely and reliably to a sequene of spatially uniform image frames with a flutuating luminane 3,43. When reordings from ells of the same type in different animals were ompared, most of the events ourred at similar times during the stimulus presentation 43. It is likely, therefore, that in the same animal multiple neurons produe spikes at similar times, resulting in synhronous volleys to the primary visual ortex 44. Neurons in layer 4 of the primary visual ortex an also fire with high preision in response to visual inputs 45,46. Neurons in the mediotemporal ortex in turn reeive inputs from the primary visual ortex and respond to motion. It has been shown that neurons in the mediotemporal ortex respond preisely to rapid hanges in the diretion of motion 47. The reliability of events in these spike trains was initially found to be low; however, a reanalysis revealed multiple reliable spike-time patterns 18. Further evidene for preise spike timing at this level is found in the barrel ortex 48 and the auditory ortex 49. Overall, the degree of preision of spiking in response to repeated presentations of the same stimulus appears to derease along the visual pathway 5, whereas spike-ount variability inreases 42,43,47, This ould be due to the presene of bakground ortial ativity, in whih ase a method to unover the stimulus-loked preision is needed (FIG. 1d). Box 1 Methods for determining the preision and reliability of spike trains The diret method In the diret method for determining spike train preision and reliablity, a spike-time histogram is onstruted, as desribed in FIG. 2. Spike alignments are lassified as events when the histogram exeeds a threshold (FIG. 2): all spikes are either assigned to an event or lassified as bakground. Event reliability is alulated diretly and event preision is the inverse of the standard deviation of all the spike times assigned to an event. Reliability and preision are the average event reliability and event preision aross all events, respetively. Indiret methods In the indiret method, statistis related to the reliability of events are alulated based on all spike times without deteting the events themselves. In one method, spike trains are transformed into a ontinuous waveform for eah trial; eah spike is onvolved with a Gaussian distribution that has a standard deviation sigma 135,136. The stronger the spike alignment between two trials, the larger the overlap between the two waveforms will be (alulated as the osine of the angle between the two waveforms when the waveforms are onsidered as vetors). This quantity is a number between (entirely different spike trains) and 1 (idential spike trains) and is alled the similarity (S ij ). The reliability estimate, R, is the mean of S ij aross all distint pairs. Intuitively, S ij measures the degree of overlap between spike times on the two trials i and j. Sigma determines whih spike times between the pairs are onsidered overlapping and sets the timesale of the similarity measure. Typially, sigma is taken to be a few milliseonds. In experimental data, the preision of the firing often varies with time. This an be dealt with by segmenting the data into small hunks and determining the R value for eah. The preision an be estimated by alulating the reliability as a funtion of sigma. The inverse of the sigma at whih R is.5 provides an estimate for the preision (FIG. 2d). Alternative measures to determine the differene between spike trains, suh as the Vitor Purpura metri 137 or the van-rossum metri 138, an be onverted to a similarity measure that is suitable for a reliability analysis. An alternative method Indiret methods always require a hoie of parameter, suh as sigma. By ontrast, the diret method yields independent estimates for the reliability and preision. An even simpler measure 115 starts with the spike times merged aross all trials and arranged with the earliest spike first. The inter-spike intervals of this sequene are then alulated and the oeffiient of variation of the aggregate response (CVP) is alulated as the standard deviation of the inter-spike intervals divided by their mean. A similarity measure normalized between (unreliable) and 1 (perfetly reliable) is obtained by subtrating 1 from the CVP and dividing by the square root of the number of trials. The ontribution of ortial osillations to preision. In addition to stimulus-related feedforward inputs, neurons in vivo are driven by internally generated network ativity. Eletroenephalograms (EEGs) reorded from the human salp exhibit superposed rhythms in various frequeny ranges, inluding the delta (.5 4 Hz), theta (4 8 Hz), alpha (8 12 Hz), beta (12 3 Hz) and gamma (3 8 Hz) ranges 54. The strength of these rhythms hanges over time and depends on behavioural states and ognitive proesses The rhythms arise from large-sale, oherent firing of neurons. Extraellular reordings of loal field potentials (LFPs) diretly from the ortex reveal bursts of osillatory ativity. These might modulate stimulus-related ativity, either diretly (by providing additional synapti inputs) or indiretly (by generating gradients in the extraellular potential 58 ), and thus might ause the apparent impreision of ortial responses desribed above. The frequeny, amplitude and phase of these ortial osillations are modulated by holinergi and GABAergi subortial projetions from the basal forebrain and from other diffuse neuromodulatory systems 59,6. A visual stimulus an reset the phase of an ongoing alpha rhythm 61, and ortial onnetions an also modify the phase of ongoing osillations 62,63. Thus, the phase and amplitude of ortial osillations an be modulated to alter the preision and timing of spike volleys. Measurements in vivo ould detet this as a modulation of both the preision of the phase-loked responses and the spike phase relative to the osillation. Evidene for phase loking in vivo. A fundamental hallenge in neurosiene is to haraterize the relationship between the input to a ortial area and the resulting output spike trains that are transmitted to other ortial areas. The relationship between the LFP and the 1 february 28 volume 9

5 Voltage (mv) Reliability Jitter (ms) Sorted trial index Sorted trial index R E V I E W S a e g All Sigma (ms) b f Sorted trial index d Segments x All Cluster number reorded spike trains is partiularly important as the LFP is dominated by subthreshold urrents that represent inputs to nearby neurons and as the spikes reflet the output of neurons that projet more distantly. Beause a periodi drive is generated at the soma during network osillations, phase-loked responses are expeted in vivo. In a landmark experiment, researhers reorded from different types of hippoampal interneurons during theta LFP osillations and sharp wave ripples (brief osillations with frequenies between 8 and 15 Hz) 67. Different interneuron types loked at speifi phases with respet to the LFP, and the phases that they loked to also depended on the frequeny of the osillation. In vivo studies have also revealed evidene for phase loking in the neoortex 57. In ortial area V4, the orrelation in the gamma frequeny range between spike trains and the LFP near the reorded neuron inreased during attention 56,57. Similarly, in a behavioural task in whih a monkey had to hold a stimulus in working memory 68, loking of spikes to the theta osillation was inreased in response to a neuron s preferred stimulus ompared with a non-preferred stimulus, independent of hanges in the neuron s firing rate. In the human brain, spike trains are also loked to the LFP in speifi frequeny bands, whih depend on the area involved 69. For example, loking to the gamma band was more prominent in the frontal region of the brain than in the parietal and temporal orties. Correlations also our between distant brain areas: the spike trains in rodent prefrontal orties orrelate with the hippoampal LFP, with approximately a 5 ms delay 7. A proedure to unover this type of phase-loking is illustrated in FIG Figure 3 Unovering spike patterns. a,b Having identified preise and reliable spike trains (see FIG. 2), spike patterns an be revealed. The value of the similarity (S ij ) between the spike train on trial i and the spike train on trial j is represented as the olour of the pixel on row i and olumn j. On the olour sale, blue indiates low similarity and red indiates high similarity.,d The rastergrams from whih the similarity matries in a and b, respetively, were alulated (the data were taken from the fourth segment (shown in yan) of FIG. 2a). In a and the trials are ordered as they are reorded, whereas in b and d they are reordered using fuzzy K means lustering 139 to bring similar trials lose to eah other 18. Spike patterns are operationally defined as groups of trials that are more similar to eah other than to the other trials. In a no obvious struture is visible, but in b spike patterns have been unovered. These patterns orrespond to square bloks, with high similarity values on the diagonal. In d eah spike pattern is shown in a different olour. The spike patterns had different spike times and, in some ases, a different number of spikes. e Reliability is the average degree of similarity between pairs of spike trains at the temporal resolution given by the parameter sigma (BOX 1). Reliability is plotted against sigma for eah spike pattern. f The jitter (the standard deviation of the spike times in an event) for eah spike pattern and aross all trials. The preision (the inverse of the jitter) that is evaluated for eah pattern separately is muh higher than that whih is alulated with all trials ombined. g Voltage traes orresponding to lusters 1 and 4. Cluster 4 spikes at 45 ms whereas luster 1 does not; at 46 ms the situation is reversed. After a transient hyperpolarization that prevents spiking, the two voltage traes are lose to onvergene at 54 ms. This graph shows that spike patterns orrespond to distint voltage trajetories 26. Phase loking and stimulus loking in the ortex. A ortial neuron reeives on the order of 1, synapti inputs 71, most of whih are from other ortial neurons and only a small fration of whih are ative at any one time. Although a stimulus waveform is loked to the stimulus onset, the phase of osillations is set internally and is therefore typially not onneted to the stimulus onset (however, in a reent in vivo experiment, the phase of ongoing delta osillations beame loked to the onset of auditory stimulation, whih was presented with an interstimulus interval that was omparable to the period of the delta osillations 63 ). The preision of firing therefore reflets a balane between intrinsi reverberations (inluding osillations) and stimulus properties 72. In a ortial model, when spikes are generated in response to stimulus-related inputs independently of those that are generated in response to osillatory inputs, stimulus-loked and phase-loked responses an be obtained at the same time (FIG. 6a,b). However, in general there will be interation between these two types of input. Depending on the nature of the interation, stimulus loking an still be obtained. For instane, stimulus loking persists when the osillatory inputs hange the number of spikes that a neuron produes in response to the stimulusrelated inputs, but not their timing (FIG. 6), or when the shift in spike times aused by the osillation is small (FIG. 6d). Single-ompartment models 73 predit a strong interation that almost surely will destroy stimulus loking nature reviews neurosiene volume 9 february 28 11

6 Neuromodulator An endogenous hemial substane that hanges the intrinsi properties of a neuron and the dynamis and strength of neurotransmission. Neuromodulators an modify neuronal responses to synapti inputs on potentially long timesales. Afterhyperpolarization The membrane hyperpolarization that follows the ourrene of one or several ation potentials. Eye-up preparation A preparation in whih the retina is extrated intat so that the neural responses to ativation of the photoreeptors by a visual stimulus an be reorded. Loal field potential (LFP). The total eletrial urrent in the viinity of the reording eletrode, refleting the sum of events in the dendrites of a loal neuronal population. It is often obtained by low-pass filtering (that is, removal of signals lower than 6 Hz ) of the reorded eletrial signal. Compartmental model A omputer model that breaks a neuron down into small eletrial ompartments and an simulate the propagation of eletrial signals inside the neuron and aross its membrane surfae. and phase loking, beause the two types of input arrive at the same ompartment. However, in ompartmental models the interation is weaker beause the synapti inputs are spatially segregated. Beause in vivo neural responses an alternate between stimulus-loked epohs and phase-loked epohs 72, averaging to extrat either the stimulus-loked or the phase-loked response should be arried out with are. Propagation of spike patterns in ortial networks The preeding setions have doumented the presene of spike patterns and phase loking at the level of individual ortial neurons. How an these patterns be retained or further proessed in ortial iruits? a Voltage (mv) Firing rate (Hz) Voltage (mv) Firing rate (Hz) Synfire hains in ortial networks. Preise spike times an lead to synhronous spike volleys in pools of neurons that an propagate from pool to pool in model 74 and in vitro 8 feedforward networks with a preision that depends on a number of physiologial parameters. The sequential ativation of multiple pools is referred to as a synfire hain (or as ortial songs 75 ). Synfire hains have been embedded in large-sale model networks by inreasing the number of synapti onnetions between seleted pools of neurons. In those networks, the synfire mode of propagation was often assoiated with large-sale wave-like ativity propagating through the network, after whih the network beame refratory 76. b Voltage (mv) Firing rate (Hz) Voltage (mv) Firing rate (Hz) d Figure 4 The effet of a periodi or an aperiodi drive on reliability in a model neuron. Eah part shows, from top to bottom, a graph with two voltage traes (the red and blak lines) and the stimulus waveform (the blue line), a rastergram and a histogram. The model neuron used in FIG. 2 provided the data. a In response to a urrent step, preision dereases over time. b When a periodi urrent is superimposed, the preision is maintained beause of a resonane effet. The firing rate is approximately the same in a and b. When the phase of the periodi drive is varied from trial to trial the preision is redued (the stimulus waveform is only shown for one phase). d In response to an aperiodi urrent, well-defined events with a range of preisions are obtained. 12 february 28 volume 9

7 a LFP b Neuron index Number of spikes Time (s) Time (s) Frequeny (Hz) Phase (degrees) STA.1 Spetrum (db) d e f Cortial pyramidal ell A lass of neuron in the erebral ortex with a pyramidshaped ell body. These neurons have dendrites that extend loally and an projet their axonal proesses both loally and distally aross many layers and brain areas...1 Delay (s) Theta Number of spikes Delta Gamma Phase (degrees) Figure 5 Unovering phase loking to internal ativity. Phase loking to internal ativity is unovered by analysing simultaneously reorded spike trains and the loal field potential (LFP) generated by a simple model. a A short segment of an example LFP trae that was onstruted by adding three noisy sinusoidal waveforms with frequenies in the gamma, theta and delta frequeny ranges. b Sample spike trains were onstruted to be weakly phase-loked, in the gamma frequeny range and at a delay of 5 ms, to the example LFP. The three peaks in the power spetrum of the example LFP reveal the presene of the frequeny ontent in gamma, theta and delta. d A histogram of the phase of the gamma osillation at the spike times shown in part. The peak (indiated by the arrow) shows that the spikes have a weak preferene for a phase of 27 degrees, whih means that they are weakly phase-loked. The histogram looks smooth beause it is averaged aross 2 neurons firing at 1 Hz during a 4-seond segment. This raises the issue of how to find groups of similarly responding neurons in multi-eletrode reordings without knowing their behaviour. The lustering proedure introdued in FIG. 3 is useful in this regard. e The spike-triggered average (STA) of the LFP is obtained by olleting, for eah spike, the LFP waveform in the interval from 12.5 ms before to 12.5 ms after the spike. The STA is the average aross all olleted waveforms. The peak (indiated by the arrow) shows that spikes are most orrelated with the LFP 5 ms in the past. f A histogram of the phase of the gamma osillation 5 ms before the spike times in part. The neuron spikes preferentially at a phase of 18 degrees. The peak is sharper than in part d, whih means that the true preision of phase loking was unovered. Another modelling study 77 determined whether information ould reliably propagate from one pool of neurons to another in the presene of internally generated bakground ativity in a random network in whih a synapti onnetion was made between a small fration of neuronal pairs. On average, a neuron reeived synapses from no more than 2% of the neurons in the network. Seven pools that were onneted in a feedforward fashion were seleted. The intrinsi properties of the neurons were parametrially varied and the onnetions between neurons in onseutive pools were strengthened (analogous to the effets of spiketiming-dependent plastiity 78 ). These studies showed that volleys either died out or propagated between pools, reruiting more spikes at eah stage. In the latter ase the timing information was lost, beause it was not possible to determine when the response to one volley ended and the response to another began. Firing-rate information was transmitted more easily when square pulses of inreased external ativity were injeted into the first pool. Firing rates modulated on a timesale of a few tens of milliseonds ould also be transmitted, but some distortions in the shape of the transmitted waveform ourred. Based on a single-ompartment model, whih assumed that the membrane potential of the entire neuron was uniform, the results suggested that in a sparse randomly onneted network it is diffiult to obtain robust and reproduible signal transmission along a synfire hain. However, real neurons are spatially extended, so the effiay of a given synapse might depend on its loation and on the onurrent ativity of other synapses in a highly nonlinear way (see below). In addition, speifi network arhitetures (that is, ones that are not sparse or random) might failitate the reproduible propagation of volleys. These two possibilities are reviewed in the following subsetions. Results that are onsistent with the existene of synfire hains have been reported in slie experiments that measured alium transients from many neurons, but diret evidene for synfire hains is still absent. Reordings have revealed repeating patterns of ativation arising from a sequene of neurons that beame ative in the same order 75. The patterns repeated more often than would be expeted from random ativation 75,79 (but see REF. 8 for an alternative view). However, the spiking preision is diffiult to determine beause individual spikes annot always be resolved. Deoding synhronous inputs in spatially extended neurons. Cortial pyramidal ells need to integrate information from many soures. For example, a layer 5 pyramidal ell 81,82 has aess to inputs from all ortial layers and must integrate these into one single spike train. Historially, dendrites have been modelled as passive strutures with a speifi resistane and a apaitane 83. However, studies over the past two deades have demonstrated the non-uniform distribution of many types of voltage-gated hannel on dendrites 84. The funtional relevane of these hannel distributions is only now starting to emerge For a passive dendrite, the voltage defletions that result from two exitatory inputs an be estimated as the sum of the individual defletions. This is an overestimate, beause the depolarization aused by the first input redues the driving fore for the seond input. Therefore, when the response atually exeeds the sum of individual responses, additional nonlinear mehanisms must be responsible. For instane, these an be based on the ativity of dendriti alium hannels and NMDA (N-methyl-d-aspartate) reeptors 85. To estimate the nonlinearity, the voltage defletion at the soma that arises from multiple inputs on the same dendriti branh of a layer 5 pyramidal ell was determined 88. When the measured response was plotted against the summed response a sigmoidal relationship was found. For weak inputs the relationship was linear 89, but for strong inputs the measured response inreased rapidly with input strength and then saturated. When the same experiment nature reviews neurosiene volume 9 february 28 13

8 Caged glutamate An inative derivative of glutamate that an be transformed into the ative transmitter, usually by photolysis. This tehnique provides an effiient means for ahieving a spatially restrited appliation of glutamate. Dendriti ation potential (dap). An ation potential that is first generated in the dendrites and whih then propagates towards the soma, often but not always eliiting a somati ation potential after a brief delay. Relay ell A type of ell in the thalamus that sends its axon to the ortex. Relay ells in the lateral geniulate nuleus reeive inputs from the retina and projet to spiny stellate ells in layer 4 of the primary visual ortex. Spiny stellate ells (SSCs). An exitatory ell type that is ommon in layer 4 of the sensory ortex. SSCs have axons that have a loal arborization pattern and have dendrites that are overed by spines. a b Firing rate (Hz) Time (s) Firing rate (Hz) Cyle index Phase (degrees) Time (s) Phase (degrees) Time (s) Figure 6 Response of a model ortial ell to stimulus-related and osillatory bakground synapti inputs. A model ell was embedded in a network produing a delta osillation. A stimulus lasting.7 seonds was presented 1, times, with a random interval between presentations. As a first approximation it was assumed that the stimulus and the osillation eliited independent preise spike patterns. a The response of the neuron aligned with the stimulus onset. b The response aligned with the osillation yle, where the x ordinate for eah spike is its phase with respet to the osillation. The top panel ontains a rastergram aross the first 5 stimulus presentations (the data in blue) and a rastergram aross the first 5 osillation yles (the data in red). The bottom panel shows the orresponding spike-time histograms aross all data, with the stimulus-related spikes in red and the osillation-related spikes in blue. When they are aligned with the stimulus onset, the stimulus-indued spikes are preise and the osillation-related spikes form a random bakground. When the data are aligned on the osillation yle the situation is reversed, with the stimulus-related spikes forming a random bakground.,d Under realisti irumstanes, there will be interation between the stimulus-related and the osillation-related synapti inputs. Two simple ases are illustrated using the stimulus-aligned spike-time histograms. The delta osillation modulated the number of spikes that were eliited by the stimulus presentation, with the higher rates ourring at the beginning of the osillation yle. The preision (the width of the peaks) was not affeted but the spike ount aross trials was muh more variable. d The delta osillation shifted the times of the stimulus-eliited spikes depending on when they ourred in the osillation yle. This redued the preision: the first two peaks seem to have merged. If stimulus-related information is to be oded in the preise spike times, the interation illustrated in part is innouous but the one in part d is harmful. Firing rate (Hz) Fining rate (Hz) d Time (s) was repeated with synapses on different branhes, the sigmoidal behaviour was absent. Apparently, eah dendriti branh integrates its input independently through a loal nonlinearity. This suggests a two step proess: first, synhrony deoding ours in the dendriti branhes, and then global integration with the inputs from other dendriti branhes at the soma follows 9. In CA1 pyramidal ells in the hippoampus, an additional faster nonlinearity is generated by the ativation of sodium hannels 91. In a landmark study, two-photon unaging of aged glutamate was used to apply a spatial pattern of synapti ativation in hippoampal slies. When a dendriti ation potential (dap) was generated at the apial trunk it quikly propagated to the soma and eliited a reliable and preise ation potential 91. When the dap was initiated in the oblique dendrites it propagated to the soma but did not lead to an ation potential 92. Instead, a rapid voltage defletion was observed at the soma, followed by a slower (but still nonlinear) defletion that was due to alium entry. In order to generate a dap, the synapti inputs to the ell needed to be both spatially lustered (within 2 µm) and temporally oherent, ourring within a few milliseonds of eah other (FIG. 7,d). Spatiotemporally oherent input at the apial trunk was also more effiient at eliiting somati ation potentials. These studies show that there are multiple ways to generate ation potentials. Some methods lead to preise spikes that are onduive to generating synhronous volleys, whereas others are more appropriate for the propagation of firing rate modulations. Gated temporal information transfer between ortial layer 4 and layer 2/3. Even though oherent synapti ativation makes feedforward propagation of spike volleys possible, inhibitory iruits and reurrent loops ould gate the propagation of spike volleys and influene their timing. Consider, for example, the feedforward pathway in the visual ortex that originates from thalamoortial relay ells that projet to layer 4 spiny stellate ells (SSCs), whih in turn projet to layer 2/3 pyramidal ells 93 (FIG. 7a). Thalamoortial synapses are more effetive than intraortial synapses 94, but they form only a small fration of the synapses onto SSCs 95, february 28 volume 9

9 b TC1 TC2 TC3 Top-down Layer 2/3 Layer 4 Asynhronous inputs dap a Feedforward dap LGN d Reurrent SSC1 SSC2 Synhronous inputs Figure 7 Experimental observations suggest that volleys that are generated by spike patterns are preferentially proessed in the early sensory ortex. a A simplified representation of the laminar struture of the feedforward pathway in ortial area V1. Thalamoortial (TC) ells projet to spiny stellate ells (SSCs) in layer 4, whih in turn projet to layer 2/3 pyramidal ells. The layer 2/3 pyramidal ells reeive feedforward input from layer 4, reurrent inputs from other pyramidal ells and top-down inputs from other ortial areas (suh as V2). In both layer 4 and layer 2/3 there is feedforward inhibitory input. The inhibitory ells and their projetions are shown in blue, whereas the exitatory ells and their projetions are shown in red. b TC ells projet to SCCs in layer 4 of the sensory ortex. Experimental reordings of TC neurons indiate the presene of spike patterns 18,43, whih suggests that there are synhronous spike volleys at the population level. The spike volleys ould be synhronous to a few SSCs (yellow highlight) or they ould be synhronous aross inputs to a large group of SSCs (red highlight). Synapses made by TC ells are more effetive than intraortial synapses, but there are fewer of them. Nevertheless, beause of synhronous spikes the TC ells as a group are effetive 98. At the ortial level, this leads to synhronous output spikes aross the SSC population when the synhrony extends aross many TC ells (red highlight), but not when it is limited to only a few TC ells (yellow highlight).,d Pyramidal ells in layer 2/3 (Ref. 14) and layer 5 (Ref. 141) of the ortex, and those in hippoampus 91,92, display dendriti ation potentials (daps) that move towards the soma where, in many ases, they lead to a preise and reliable output spike. Experiments in the hippoampus that used aged glutamate established the onditions under whih dap are generated 91. dap were not obtained when a pyramidal ell was stimulated by asynhronous spike trains. Target synapses are depited as red irles. d dap were obtained when the input spike trains were synhronous and the synapses they ativated were lose together (lustered) on the dendrite (arrow 1; synapti distane less than 2 µm ); they were not obtained when the synapses were further apart (arrow 2; synapti distane more than 2 µm). LGN, lateral geniulate nuleus. dap 1 2 dap Nevertheless, olletively they seem to be effiient in driving the SSCs 45,97. The reason for this effiieny was eluidated in another ortial area, in neurons that projet from the ventroposteromedial thalamus (VPM) to the barrel ortex 98 and that respond to whisker movement. Membrane defletion in a SSC in response to a single spike in a presynapti thalamoortial neuron was small ompared to the depolarization that was aused by sensory events. Nevertheless, beause rapid whisker defletions aused synhronous thalamoortial spikes, the SSC spiked reliably (FIG. 7b). The authors estimated that approximately 3 of the 85 thalamoortial ells that projeted to a given ell were simultaneously ative 98. Simulations of the impat of synhronous thalami inputs to a detailed ompartmental model of a reonstruted SSC onfirmed the experimental findings and further revealed the importane of having balaned bakground inputs from other ortial ells 99. The experimentally observed spike patterns in the lateral geniulate nuleus orrespond at the population level to synhronous volleys. Taken together with experimental results from other sensory modalities 48,1, this suggests that the output of SSCs might also onsist of spike volleys. In the at primary visual ortex, the response of thalamoortial ells to a briefly flashed square was ompared to the response of layer 4 and layer 2/3 ortial ells 11. The layer 4 response was reliable, but the layer 2/3 response was less reliable. Evidene for the role of inhibition in synapti transmission from layer 4 to layer 2/3 is found in slie experiments in the rodent barrel ortex Taken together, these experiments point to the presene of a gating mehanism between layer 4 and layer 2/3, under the ontrol of inhibition, that allows some signals but not others to propagate. At present, only the exitatory pathway has been studied in biophysially onstrained models 16. The laminar struture of the ortex 93,17, in whih various reurrent loops are present, might have advantages for proessing and transmitting sensory information in the form of spike times as suggested in a reent modelling study 18. Inhibition an modulate firing rate and influene spike times. Preise inhibition generated by fast ortial osillations an gate and modulate the propagation of spike volleys. Cortial basket ells make synapses lose to or diretly onto the soma of pyramidal ells. In the hippoampus, the spike of one basket ell an synhronize the ativity of a large number of pyramidal ells 19. Inhibitory ells are involved in the generation of fast osillations, espeially those in the gamma frequeny range 11,111. Consistent with this role, for in vivo reordings the power spetrum of urrents generated by inhibitory synapses has more power in the gamma frequeny range than the power spetrum of urrents generated by exitatory synapses 112. To test the impat of inhibitory urrents on neural spiking, urrents representing inhibitory and exitatory inputs were injeted at the soma using the dynami lamp tehnique 112. The properties of the injeted urrent were adjusted so that the overall response properties of the neurons in vitro were the same as those of similar neurons in vivo. First the nature reviews neurosiene volume 9 february 28 15